Frequency polygons

Also, frequency polygons and histograms as well as frequency tabulation were displayed for each variable. 

Frequency polygons emphasize the form of a frequency distribution by joining the co-ordinates with straight lines, in contrast to a histogram. This is particularly useful when plotting two or more sets of data values on the same graph. 

A modification of the histogram display of differences is a plot suggested by Krouwer and Mont)P Icnown as the mountain plot. This is a plot of cumulative frequencies (c/%) of differences up to 50% with subsequent subtracted cumulative frequencies (100% - cf%). Such a plot shows in principle the same information as a histogram or frequency polygon plot. An advantage may be that the percentiles can be directly read from the plot. 

Consider the set of data below, which represents polychlorinate biphenyl (PCB) levels in a contaminated water stream for a given hour for 25 days. As a first step in summarizing the data, you are requested to form a frequency table, a frequency polygon, a cumulative frequency table, and a cumulative frequency distribution curve. 

As a further step, one can graph the information in the frequency table. One way of doing this would be to plot the frequency midpoint of the class interval. The solid line connecting the points of Figure 129 forms a frequency polygon. 

Figure 129. Pollution concentration (midpoint of class interval) frequency polygon.

Figure 2.15. Sieve test data plotted on arithmetic graph paper - percentage by weight of the fractions retained between two given sieves in the B.S. series a) the frequency polygon b) the frequency histogram...

The cumulative frequency distribudon can also be disph ed using a histogram or a cumulative frequency polygon, as shown in Figures 19.2 and 19.3, respectively. These figures... 

For Problem 19.1, calculate the cumulative frequency and plot a cnunularive-frequency polygon. 

Figure 3.12. Frequency of various polygonal faces in grains, cells and bubbles (after C.S. Smith,...

Figure 9. Density of states of a water sample, referring to three-, four-, five- and six-member polygons and to the total of the sample (from top to bottom), as resulting from MD simulation, T=305 K. Dotted lines indicate vibrational frequencies for a single water molecule in gas phase.

Frequency of polygonal faces with different numbers of edges. Data from C. S. Smith, in Metal Interfaces (Cleveland, OH ASM, 1952). Reprinted with permission from ASM International . All rights reserved. www.asminternational.org. 

If the original polygon is sampled from a sinusoid of spatial frequency ui = 1/m where m is the number of polygon points per complete cycle, so that P0[j] = cos(2njcj), j G Z, the result of multiplying by the sampling matrix can be expressed as... 

With a non-stationary scheme, however, for a given initial spatial frequency of polygon, (i.e. a fixed known number of vertices per complete cycle, or vertices forming a regular polygon), the coefficients can vary at each step so that the halving relative frequency of the signal is tracked by a zero of the kernel. 

The artifact behaviour tends to be dominated by the earlier steps, because after each step the intended spatial frequency is halved relative to the density of vertices along the polygon. Because low spatial frequencies have little artifact effect, the later steps do not cause much distortion. 

A Computer-oriented algorithm for nonstationary random vibrations of polygonal Kirchhoff-plates has been developed. A fast and accurate BEM for calculation of undamped frequency response function has been used. Light hysteretic damping has been introduced subsequently, and the modified spectral Priestley-formulation has been applied in order to calculate evolutionary output power spectral density functions. It is hoped that this solution strategy will be of interest for workers in the field of probabilistic structural dynamics. 

Seismic Network and Data Quaiity, Fig. 3 Frequency-amplitude plot for octave-wide band passes of ground-motion acceleration. The blue polygon represents the sensitivity limits of an STS-2 broadband seismometer, where the frequency limit at 50 Hz is given by the Nyquist frequency for a sample rate of 100 Hz. The lower acceleration amplitude limit in the band 0.001-50 Hz is the minimum sensitivity of the sensor,... 

---